Designs of experiments are often used in studying the effects of multiple input variables upon one or more output variables, such as the quantifiable output of a particular process. For example, designs of experiments can be used in testing the effects of various environmental conditions upon the operation of a particular apparatus, such as a gas turbine engine. In such an example, the input variables can represent certain quantifiable conditions, such as altitude and inlet pressure, and the output variables can represent quantifiable measures representing the operation of an apparatus, such as the exhaust gas temperature of a gas turbine engine. Designs of experiments often use linear models to approximate the relationship between the input variables and the output variables.
Often a design of experiments is conducted by running a series of experiments on an apparatus such as a gas turbine engine. In such experiments, the input variables representing the environmental conditions are systematically altered, and the corresponding effects on the output variables are recorded. However, in many circumstances the physical apparatus may be costly to obtain and/or not readily available. Moreover, it is often difficult, costly and time consuming to properly configure the testing so that the input variables represent the entire range of environmental conditions, and to perform the testing and collect the data from the results of all of the tests to obtain complete and accurate results in the experiments on the apparatus.
An alternative approach, using an accurate model as a proxy for the apparatus, can save a significant amount of time and money with little loss of accuracy, depending on the accuracy of the baseline model. However, frequently the available models are too complex and/or cumbersome to run efficiently, often relying on thousands of data points, and taking weeks or months to run, for example in the case of available finite element models for gas turbine engines. Other available models, such as linear regression models, may not provide a very accurate fit for the data, particularly for nonlinear relationships among the variables.
Accordingly, there is a need for an improved design of experiments for modeling relationships between input variables and output variables associated with the operation of an apparatus or other process, such as the operation of a gas turbine engine, that is more accurate, time effective and/or cost effective than existing models, that does not require running new tests on the apparatus or process, and that does not have the limitations of a linear regression model.